Related papers: A Gauss Elimination Method for Resonances
As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not…
Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (L-plane). Another formulation complementing these two approaches was…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…
Starting with a general discussion, a program is sketched for a quantization based on dilations. This resolving-power quantization is simplest for scalar field theories. The hope is to find a way to relax the requirement of locality so that…
The gravitational potential is a key function involved in many astrophysical problems. Its evaluation inside continuous media from Newton's law is known to be challenging because of the diverging kernel 1/|r-r'|. This difficulty is…
An technique is extended to estimate some critical exponents without using the expansion over the coupling constant. The data obtained is in a agreement with those found by help of the 2D Onsager method or with recent 3D results. In the…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an…
The Gauss-Jordan elimination algorithm is extended to reduce a row-finite $\omega\times\omega$ matrix to lower row-reduced form, founded on a strategy of rightmost pivot elements. Such reduced matrix form preserves row equivalence, unlike…
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution…
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…